/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [isQid](x0) = x0, [and](x0, x1) = 2x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 2, [a] = 4, [a__isPal](x0) = 2x0, [isPal](x0) = 2x0, [a__isNePal](x0) = x0, [isNeList](x0) = x0, [a__isQid](x0) = x0, [isList](x0) = x0, [a__isNeList](x0) = x0, [a__isList](x0) = x0, [a__and](x0, x1) = 2x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = 2x0 + x1, [__](x0, x1) = 2x0 + x1 orientation: a____(__(X,Y),Z) = 4X + 2Y + Z >= 2X + 2Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 2X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__and(tt(),X) = X >= X = mark(X) a__isList(V) = V >= V = a__isNeList(V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isList(V1),isList(V2)) a__isNeList(V) = V >= V = a__isQid(V) a__isNeList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) = V >= V = a__isQid(V) a__isNePal(__(I,__(P,I))) = 3I + 2P >= 2I + 2P = a__and(a__isQid(I),isPal(P)) a__isPal(V) = 2V >= V = a__isNePal(V) a__isPal(nil()) = 0 >= 0 = tt() a__isQid(a()) = 4 >= 0 = tt() a__isQid(e()) = 2 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a____(mark(X1),mark(X2)) mark(and(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__and(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(isPal(X)) = 2X >= 2X = a__isPal(X) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 4 >= 4 = a() mark(e()) = 2 >= 2 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) a__and(X1,X2) = 2X1 + X2 >= 2X1 + X2 = and(X1,X2) a__isList(X) = X >= X = isList(X) a__isNeList(X) = X >= X = isNeList(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) a__isPal(X) = 2X >= 2X = isPal(X) problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 6x0 + 1, [isQid](x0) = 4x0, [and](x0, x1) = x0 + x1, [u] = 0, [o] = 4, [i] = 2, [e] = 0, [a] = 0, [a__isPal](x0) = 6x0 + 1, [isPal](x0) = 6x0 + 1, [a__isNePal](x0) = 6x0 + 1, [isNeList](x0) = 4x0, [a__isQid](x0) = 4x0, [isList](x0) = 4x0, [a__isNeList](x0) = 4x0, [a__isList](x0) = 4x0, [a__and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__and(tt(),X) = X >= X = mark(X) a__isList(V) = 4V >= 4V = a__isNeList(V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 4V1 + 4V2 >= 4V1 + 4V2 = a__and(a__isList(V1),isList(V2)) a__isNeList(V) = 4V >= 4V = a__isQid(V) a__isNeList(__(V1,V2)) = 4V1 + 4V2 >= 4V1 + 4V2 = a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) = 4V1 + 4V2 >= 4V1 + 4V2 = a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) = 6V + 1 >= 4V = a__isQid(V) a__isNePal(__(I,__(P,I))) = 12I + 6P + 1 >= 4I + 6P + 1 = a__and(a__isQid(I),isPal(P)) a__isPal(V) = 6V + 1 >= 6V + 1 = a__isNePal(V) a__isPal(nil()) = 1 >= 0 = tt() a__isQid(i()) = 8 >= 0 = tt() a__isQid(o()) = 16 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2) mark(isList(X)) = 4X >= 4X = a__isList(X) mark(isNeList(X)) = 4X >= 4X = a__isNeList(X) mark(isQid(X)) = 4X >= 4X = a__isQid(X) mark(isNePal(X)) = 6X + 1 >= 6X + 1 = a__isNePal(X) mark(isPal(X)) = 6X + 1 >= 6X + 1 = a__isPal(X) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 2 >= 2 = i() mark(o()) = 4 >= 4 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2) a__isList(X) = 4X >= 4X = isList(X) a__isNeList(X) = 4X >= 4X = isNeList(X) a__isQid(X) = 4X >= 4X = isQid(X) a__isNePal(X) = 6X + 1 >= 6X + 1 = isNePal(X) a__isPal(X) = 6X + 1 >= 6X + 1 = isPal(X) problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [isQid](x0) = x0, [and](x0, x1) = 2x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 2, [a__isPal](x0) = x0, [isPal](x0) = x0, [a__isNePal](x0) = x0, [isNeList](x0) = x0, [a__isQid](x0) = x0, [isList](x0) = x0, [a__isNeList](x0) = x0, [a__isList](x0) = x0, [a__and](x0, x1) = 2x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = 4x0 + x1 + 1, [__](x0, x1) = 4x0 + x1 + 1 orientation: a____(__(X,Y),Z) = 16X + 4Y + Z + 5 >= 4X + 4Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 4X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__and(tt(),X) = X >= X = mark(X) a__isList(V) = V >= V = a__isNeList(V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 4V1 + V2 + 1 >= 2V1 + V2 = a__and(a__isList(V1),isList(V2)) a__isNeList(V) = V >= V = a__isQid(V) a__isNeList(__(V1,V2)) = 4V1 + V2 + 1 >= 2V1 + V2 = a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) = 4V1 + V2 + 1 >= 2V1 + V2 = a__and(a__isNeList(V1),isList(V2)) a__isNePal(__(I,__(P,I))) = 5I + 4P + 2 >= 2I + P = a__and(a__isQid(I),isPal(P)) a__isPal(V) = V >= V = a__isNePal(V) a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(and(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__and(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(isPal(X)) = X >= X = a__isPal(X) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 2 >= 2 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(X1,X2) a__and(X1,X2) = 2X1 + X2 >= 2X1 + X2 = and(X1,X2) a__isList(X) = X >= X = isList(X) a__isNeList(X) = X >= X = isNeList(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) a__isPal(X) = X >= X = isPal(X) problem: a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isNeList(V) -> a__isQid(V) a__isPal(V) -> a__isNePal(V) a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [and](x0, x1) = x0 + [0 1 0]x1 + [0] [0 0 0] [0], [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [a__isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 1 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [a__isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 1 0] [1] [a__isList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 1 0] [1] [a__and](x0, x1) = x0 + [0 1 0]x1 + [0] [0 0 0] [0], [0] [tt] = [0] [1], [0] [nil] = [0] [0], [1 1 0] [0] [mark](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 1] [0] [a____](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 1] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 1 0] [1] [1 1 0] [0] a__and(tt(),X) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [0] a__isList(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = a__isNeList(V) [0 0 0] [1] [0 0 0] [1] [1] [0] a__isList(nil()) = [1] >= [0] = tt() [1] [1] [1 0 0] [0] [1 0 0] [0] a__isNeList(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = a__isQid(V) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] a__isPal(V) = [0 0 0]V >= [0 0 0]V = a__isNePal(V) [0 0 0] [0 0 0] [0] [0] a__isQid(u()) = [1] >= [0] = tt() [1] [1] [1 1 0] [1 1 1] [1] [1 1 0] [1 1 0] [1] mark(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = a____(mark(X1),mark(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] mark(and(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = a__and(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1] [1 1 0] [1] mark(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] mark(isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] mark(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isQid(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__isNePal(X) [0 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__isPal(X) [0 0 0] [1] [0 0 0] [0] [0] mark(nil()) = [0] >= [0] = nil() [1] [0] [0] [0] mark(tt()) = [0] >= [0] = tt() [1] [1] [0] [0] mark(a()) = [0] >= [0] = a() [1] [0] [0] [0] mark(e()) = [0] >= [0] = e() [1] [0] [0] [0] mark(i()) = [0] >= [0] = i() [1] [0] [0] [0] mark(o()) = [0] >= [0] = o() [1] [0] [0] [0] mark(u()) = [0] >= [0] = u() [1] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] a____(X1,X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] a__and(X1,X2) = X1 + [0 1 0]X2 + [0] >= X1 + [0 1 0]X2 + [0] = and(X1,X2) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [0] a__isList(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(X) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] a__isNeList(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNeList(X) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] a__isQid(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] problem: a__isNeList(V) -> a__isQid(V) a__isPal(V) -> a__isNePal(V) a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [1], [0] [u] = [1] [1], [0] [o] = [1] [1], [0] [i] = [1] [0], [0] [e] = [0] [0], [1] [a] = [0] [0], [1 0 0] [1] [a__isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [1] [a__isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [a__isList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [1 0 0] [0] [a__and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [1], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 1 0] [0] [mark](x0) = [1 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [0] [a____](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 0 1] [1] [1 0 1] a__isNeList(V) = [0 0 0]V + [0] >= [0 0 0]V = a__isQid(V) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] a__isPal(V) = [0 0 0]V + [0] >= [0 0 0]V = a__isNePal(V) [0 0 0] [0] [0 0 0] [1] [0] a__isQid(u()) = [0] >= [0] = tt() [0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [0] mark(__(X1,X2)) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = a____(mark(X1),mark(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(and(X1,X2)) = [1 1 0]X1 + [1 0 0]X2 + [1] >= [1 1 0]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isList(X)) = [1 0 0]X + [1] >= [0 0 0]X + [0] = a__isList(X) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] mark(isNePal(X)) = [1 0 0]X + [0] >= [0 0 0]X = a__isNePal(X) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isPal(X)) = [1 0 0]X + [1] >= [0 0 0]X + [0] = a__isPal(X) [0 0 0] [1] [0 0 0] [0] [0] [0] mark(nil()) = [0] >= [0] = nil() [1] [0] [0] [0] mark(tt()) = [0] >= [0] = tt() [1] [0] [1] [1] mark(a()) = [1] >= [0] = a() [1] [0] [0] [0] mark(e()) = [0] >= [0] = e() [1] [0] [1] [0] mark(i()) = [1] >= [1] = i() [1] [0] [1] [0] mark(o()) = [1] >= [1] = o() [1] [1] [1] [0] mark(u()) = [1] >= [1] = u() [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] a____(X1,X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] a__and(X1,X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1] [1 0 1] a__isNeList(X) = [0 0 0]X + [0] >= [0 0 0]X = isNeList(X) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 1] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] a__isPal(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1] [e] = [0] [0], [0] [a] = [1] [0], [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a__isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a__isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [1] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [1 0 0] [1 1 0] [1] [a____](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [0] [0 1 0] [0 0 0] [1], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] mark(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isNePal(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] mark(isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X = a__isPal(X) [0 0 0] [0] [0 0 0] [0] [0] mark(nil()) = [1] >= [0] = nil() [0] [0] [0] [0] mark(tt()) = [1] >= [0] = tt() [0] [0] [0] [0] mark(a()) = [1] >= [1] = a() [1] [0] [1] [1] mark(e()) = [1] >= [0] = e() [0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] a____(X1,X2) = [0 1 1]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 1 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 1 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__isNePal(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [0] [e] = [0] [1], [0] [a] = [1] [0], [1 1 0] [1] [a__isPal](x0) = [1 1 0]x0 + [1] [1 0 0] [1], [1 0 0] [1] [isPal](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [1 1 0] [0] [a__isNePal](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [a__isList](x0) = [0 0 0]x0 + [0] [1 0 0] [1], [1 0 0] [1 0 0] [0] [a__and](x0, x1) = [0 0 1]x0 + [1 0 0]x1 + [1] [0 1 0] [1 0 0] [0], [0] [tt] = [0] [1], [0] [nil] = [1] [0], [1 1 1] [mark](x0) = [1 1 0]x0 [1 0 1] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] mark(and(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [1] >= [1 0 1]X1 + [1 0 0]X2 + [1] = a__and(mark(X1),X2) [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] [1 0 0] [1] [1 0 0] [0] mark(isList(X)) = [1 0 0]X + [0] >= [0 0 0]X + [0] = a__isList(X) [1 0 0] [1] [1 0 0] [1] [1 1 0] [1] [1 1 0] [0] mark(isNePal(X)) = [1 1 0]X + [1] >= [1 0 0]X + [1] = a__isNePal(X) [1 1 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(isPal(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = a__isPal(X) [1 0 0] [1] [1 0 0] [1] [1] [0] mark(nil()) = [1] >= [1] = nil() [0] [0] [1] [0] mark(tt()) = [0] >= [0] = tt() [1] [1] [1] [0] mark(a()) = [1] >= [1] = a() [0] [0] [1] [0] mark(e()) = [0] >= [0] = e() [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] a__and(X1,X2) = [0 0 1]X1 + [1 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 1 0] [1 0 0] [0] [0 1 0] [0 0 0] [0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] a__isNePal(X) = [1 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] a__isPal(X) = [1 1 0]X + [1] >= [0 1 0]X + [0] = isPal(X) [1 0 0] [1] [0 0 0] [0] problem: mark(isPal(X)) -> a__isPal(X) a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [1 0 0] [1] [1 0 0] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__isPal(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [a__isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isPal(X) = [0 0 0]X + [0] >= [0 0 0]X = isPal(X) [0 0 0] [0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [a__isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isNePal(X) = [0 0 0]X + [0] >= [0 0 0]X = isNePal(X) [0 0 0] [0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) a__isQid(X) -> isQid(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [a__isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isQid(X) = [0 0 0]X + [0] >= [0 0 0]X = isQid(X) [0 0 0] [0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed